# How to Calculate NPV with Taxes

In this article, I will show you how to calculate the net present value of a project when

**taxes are taken into consideration.**So the first thing we're going to do is we're going to take all the cash flows of the project and we're going to convert them to an**after-tax basis**using the company's tax rate then we're gonna**discount all the cash flows**to their present value just like you would with a normal NPV problem.So let's take this problem right here as an example

So we've got a pizzeria that pays

**$60,000**cash today to buy a pizza oven and then they're gonna use that oven to generate**$20,000**of cash flow each of the next**4 years**they're gonna**depreciate**the oven taking**$15000**of depreciation every year and at the end of**year 4**they're gonna sell the oven for**$6000**and they've got an income tax rate of**21%**and then a discount rate of**8%**that we'll use to find the**present values.**

So let's work on this problem. So in period zero which is today, we're gonna have a negative

**-$60,000**we're not gonna have to discount that or worry about after-tax or anything like that. So let's move now to**period one**we're gonna receive**$20,000**but remember we're gonna have to pay tax on this**$20,000**we're receiving. So you take**$20,000**and multiply it by**(1 - the tax rate)**. One minus**21%**so it is**79%**and that's gonna give you**$15,800.**

So we're gonna put

**$15,800**in**period 1**and here's what this means we receive**$20,000**of cash however we had to**pay tax**on that money at**21%**and if you calculate the tax and subtracted it from the**$20,000**you would give**$15,800.**Now we're also going to get a tax deduction for the**depreciation.**Now normally in real life depreciation would not be the same amount every single year because for tax purposes usually you have**accelerated depreciation**where you take more depreciation in the early years of the asset but to make this problem simple we're just gonna say**$15,000**every year for**4 years.** So we're gonna take that

**$15,000**and we need to know what is the value of that**tax deduction**because that deduction is going to**reduce the amount of tax**we have to pay and how do we figure that out? Well we multiply it by our tax rate**21%.**So**$15,000**times**21%**is**$3,150.**So our cash flows on an after-tax basis for the very first period we'd have**$18,950.**

Another way of getting that well I'm just going to take

**$20,000**of income that we had, subtract the**$15,000**of deduction the tax deduction of depreciation, then**$20,000**minus**$15,000**would mean you'd have**$5000**of**taxable income**you multiply that by**21%**which is**($5000****x 21% = $1,050)**that means you'll have to pay in the first year**$1,050**in taxes. So this would be a**cash outflow**for taxes but you receive**$20,000**so**$20,000**minus the tax you pay of**$1,050**that would also give you**$18,950.**

So I'm just saying there's just there's a couple different ways to do it. Now but I'm just going to continue with the first way where we're converted the after-tax cash flows first. So for the second year we're also gonna receive

**$20,000**but after we multiply by**(1 - the tax rate)**that's**$15,800**and again we're gonna have this depreciation to reap. By the way if you don't understand why I'm doing this**($15,000 X 21%)**remember that although depreciation is a non-cash, like it doesn't it's not like we're getting cash but by depreciating an asset we're getting a tax deduction of**$15,000**and that's saving us or we don't have to pay**$3,150**of taxes. Okay so if you're thinking about well depreciation is not a cash flow why are you doing this it's because it's giving us a**tax break**and we're saving**$3,150**of taxes. So again we're gonna have**$18,950.**So the these here are after-tax cash flows remember I said that's the first step we're going to do convert to after-tax basis and I'm for the**third period**they're the same thing**$18,950.**The

**fourth year**we've got one little different so we got**$15,800**we've got**$3,150**but then we also sell a machine we have a gain of**$6000**that's going to be taxed, we take**$6000**times**(1 - the tax rate)**which will be**79%**so that means that we're gonna get**$4,740**after we pay tax on that gain. we're gonna receive four thousand seven hundred and forty dollars. So I'll add it too then we'll get**$23,690.**We're gonna discount each of these to the

**present value.**So these after tax cash flows now we need to discount them remember our discount rate is**8%**So divided by**(1.08)**to the first power. Why am I doing that? Well you take your**cash flow**divided by**(1+ the discount rate)**to the**n'th power,**where**n**is**the period.** So we're gonna divide the

**year two**cash flows divided by**(1.08)**to the**second power,**here you've**3rd year**cash flows divided by**(1.08)**to the**third power**and then here**4th year**cash flows divided by**(1.08)**to the**fourth power.**So now here our

**after tax cash flows**and we discount this**$18,950**divided by**(1.08)**to the first power so that comes out to**$17546**then the 2nd one this one is**$16,247**and then 3rd one is**$15,043,**okay? and then last number 4th one here is**$17,413.**Now if we add them across we get to**$6249**that is the net present value of this project now because the project has a positive net present value the NPV is**greater than zero**assuming the company has the capital to do this project, they should accept the project.
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